Solutions to Monge-Kantorovich equations as stationary points of a dynamical system
arXiv:math/0507330
Abstract
Solutions to Monge-Kantorovich equations, expressing optimality condition in mass transportation problem with cost equal to distance, are stationary points of a critical-slope model for sand surface evolution. Using a dual variational formulation of sand model, we compute both the optimal transport density and Kantorovich potential as a stationary limit of evolving sand flux and sand surface, respectively.
7 pages, 3 figures